The solution set of the quadratic inequality x squared minus 5 x plus 4 less or equal than 0 is

9514 1404 393

Answer:

  a) no

  b) yes

  c) yes

  d) no

Step-by-step explanation:

Angle LJM is complementary to KJL, so is ...

  angle LJM = 90° -42° = 48°

Angle NJP is marked as congruent to angle PJQ, so is also 48°.

__

a) ∠KJL = 42° ≠ 48° = ∠LJM . . . . NO

b) ∠MJP = 46°+48° = 48° +46° = ∠PJR . . . . YES

c) ∠LJP = 48° +46° +48° = 48° +48° +46° = ∠NJR . . . . YES

d) ∠MJK = 90° ≠ 48° +46° = ∠PJR . . . . NO

Answer:

x = 29

Step-by-step explanation:

The angles are corresponding angles and corresponding angles are equal when the lines are parallel

3x+17 = 4x-12

Subtract 3x from each side

3x+17-3x = 4x-12-3x

17 = x-12

Add 12 to each side

17+12 = x-12+12

29 =x

Answer:

D. 29

Step-by-step explanation:

If you plug in 29 in the missing values for L1 and L2, you get

L1 = 3(29) + 17 = 104

L2 = 4(29) - 12 = 104

I know I am correct because since both L1 and L2 are parallel and T in cutting them, I know that they are both going to be the same degrees, 104.

So, your answer would be D. 29

Hope the helps! :)

Answer:

Step-by-step explanation:

y varies direcrtly with √(x+5) wich can be expressed mathematically as:

● y = k*√(x+5)

Let's calculate k khowing that y=4 and x=-1

● 4 = k*√(-1+5)

● 4 = k*√(4)

● 4 = k * 2

● k = 4/2

● k = 2

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's calculate y khowing that x = 11

● y = k*√(x+5)

● y = 2×√(11+5)

● y = 2× √(16)

● y = 2× 4

● y = 8

Answer:

The value of y is 8.

Step-by-step explanation:

Given that y is directly proportional to √(x+5) so the equation is y = k√(x+5) where k is constant. First, you have to find the value of k with given values :

[tex]y = k \sqrt{x + 5} [/tex]

[tex]let \: x = - 1,y = 4[/tex]

[tex]4 = k \sqrt{ - 1 + 5} [/tex]

[tex]4 = k \sqrt{4} [/tex]

[tex]4 = k(2)[/tex]

[tex]4 \div 2 = k[/tex]

[tex]k = 2[/tex]

So the equation is y = 2√(x+5). In order to find the value of y, you have to substitute x = 11 into the equation :

[tex]y = 2 \sqrt{x + 5} [/tex]

[tex]let \: x = 11[/tex]

[tex]y = 2 \sqrt{11 + 5} [/tex]

[tex]y = 2 \sqrt{16} [/tex]

[tex]y = 2(4)[/tex]

[tex]y = 8[/tex]

Answer:

The 2 Gallon Tank is Enough

Step-by-step explanation:

A drink bottler needs to bottle 16 one-pint bottles. He has a 2 gallon tank and a 3 gallon tank.

There are 8 pints in a gallon. This means that 2 gallons would be 16 pints.

[tex]8 * 2 = 16[/tex]

So, the 2 gallon tank has 16 pints, which means that the 2 gallon tank should be enough to bottle all 16 bottles.

Answer:

2 gallon tank

Step-by-step explanation:

16 pints is the same as 2 US gallons

Answer: A) 0

P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.

We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.

Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)=0.99   using the cumulative standard normal distribution table

Answer:

6.642

Step-by-step explanation:

Given that mean = 2

standard deviation = 2

Let X be the random Variable

Then X [tex]\sim[/tex] N(n,[tex]\sigma[/tex])

X [tex]\sim[/tex] N(2,2)

By Central limit theorem;

[tex]z = \dfrac{X - \mu}{\sigma} \sim N(0,1)[/tex]

[tex]z = \dfrac{X - 2}{2} \sim N(0,1)[/tex]

P(X<x) = 0.09

[tex]P(Z < \dfrac{X-\mu}{\sigma })= 0.99[/tex]

[tex]P(Z < \dfrac{X-2}{2})= 0.99[/tex]

P(X < x) = 0.99

[tex]P(\dfrac{X-2}{2}< \dfrac{X-2}{2})=0.99[/tex]

[tex]P(Z< \dfrac{X-2}{2})=0.99[/tex]

[tex]\phi ( \dfrac{X-2}{2})=0.99[/tex]

[tex]( \dfrac{X-2}{2})= \phi^{-1} (0.99)[/tex]

[tex]( \dfrac{X-2}{2})= 2.321[/tex]

X -2 = 2.321 × 2

X -2 = 4.642

X = 4.642 +2

X = 6.642

Answer:

Step-by-step explanation:

This is an example of a frequency distribution for a class interval. In order to complete the frequency distribution, we will count the number of data occurring in each group, and write that number as the frequency for that group. This is done as shown below:

 Age                Frequency          ages in class

20-29                       4                  22, 26, 27, 27                

30-39                       3                  31, 34, 36

40-49                       5                  42, 43, 44, 48, 49

50-59                       5                  52, 53, 55, 56, 57

60-69                       6                  60, 56, 65, 66, 67, 69

70-79                        6                  72, 75, 77, 78, 78, 79

80-89                       1                   87

Total                        30

x= 30 degrees

Step-by-step explanation:

there's 180 degrees in a triangle. You can see 60 degrees right there. Theres a 90 degree angle right next to it. 180-150=30

This requires finding the number of small sweaters the company made last week

Number of small sweaters the company produced last week is 372

Total sweaters made = 1,612

Let

Small sweaters = 3x

Medium sweaters = x

Large sweaters = 3(3x) = 9x

Total = small + medium + large

1,612 = 3x + x + 9x

1612 = 13x

Divide by 13

x = 1612/13

Medium sweaters = x = 124

Small sweaters = 3x

= 3(124)

= 372

Read more:

https://brainly.com/question/24326559

Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The x-coordinate is measured in minutes since the tank began to be filled and the y-coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

[tex]\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1[/tex]

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

[tex]\displaystyle y - y_1 = m( x - x_1)[/tex]

Where m is the slope/rate of change and (x₁, y₁) is a point.

We will substitute 0.1 for m and let (10, 4.8) be the point. Hence:

[tex]\displaystyle y - (4.8) = 0.1(x - 10)[/tex]

Simplify:

[tex]\displaystyle y = 0.1(x-10) + 4.8[/tex]

Since y represent how full the tank is and x represent the time in minutes since the tank began to be filled, we can substitute y for V(t) and x for t. Thus, our function is:

[tex]\displaystyle V(t) = 0.1(t - 10) + 4.8[/tex]

The initial volume is when t = 0. Evaluate:

[tex]\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8[/tex]

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for t. Hence:

[tex]60 = 0.1(t - 10) + 4.8[/tex]

Subtract:

[tex]55.2 = 0.1(t - 10)[/tex]

Divide:

[tex]552 = t - 10[/tex]

Add. Therefore:

[tex]t = 562\text{ minutes}[/tex]

It will take 562 minutes for the tank to be completely filled.

Answer:

The x-intercepts are at (-4, 0) and (3, 0). The y-intercept is at (0, 1.2).

The graph is increasing at (-4, 0), (2.082, -0.604), (3, 0).

The graph is decreasing at (-2.082, 3.004), (0, 1.2), (1, 0)

Step-by-step explanation:

Answer:

The length is 46.05551275 inches, and the width is 26.05551275 inches.

Step-by-step explanation:

We know that the area must be 1200 square inches. Using this information, we can create an equation, where x is length and y is width:

x*y=1200

We know that its length must be 20 inches longer than its width. Therefore, x=y+20. Using this new information, we can replace 'x' in 'x*y=1200' with 'y+20':

(y+20)*y=1200

[tex]y^{2} +20y=1200[/tex]

[tex]y^{2} +20y-1200=0[/tex]

I have decided to use the quadratic formula, but you could also factor this equation into the 'intercept' form to determine the roots, which ultimately provides the same answer.

[tex]y=\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex]

[tex]y=\frac{-(20)+\sqrt{(20)^{2} -4(1)(-1200)} }{2(1)}[/tex]

[tex]y=\frac{-(20)+\sqrt{400+4800} }{2}[/tex]

[tex]y=\frac{-(20)+\sqrt{5200} }{2}[/tex]

[tex]y=\frac{52.11102551 }{2}[/tex]

[tex]y=26.05551275[/tex] inches

[tex]x=y+20[/tex]

[tex]x=(26.05551275)+20[/tex]

[tex]x=46.05551275[/tex] inches

Therefore, the length is 46.05551275 inches, and the width is 26.05551275 inches.

Answer:

Step-by-step explanation:

Answer:

Length = 21.3333333333;   Width: 12.6666666667

Step-by-step explanation:

Perimeter = 68

Perimeter of a rectangle:

2 (L +W)

Length (L) = 2W - 4

Width = W

2 ( 2W -4 +W) = 68

=> 2 (3W - 4) = 68

=> 6w -8 = 68

=> 6w = 76

=> w = 12.6666666667

Length = (12.6666666667 X 2) - 4

=> 21.3333333333

Answer:

B - %9230.77

Step-by-step explanation:

the original price of the fencing before the trade discount was approximately $9,230.77.

To find the original price of the fencing before the trade discount, we need to calculate the amount that corresponds to a 35% decrease from the discounted price.

Let's denote the original price as "P". The discounted price is given as $6,000.

The discounted price is calculated by subtracting the discount amount from the original price:

Discounted price = Original price - Discount amount

The discount amount is determined by multiplying the original price by the discount rate:

Discount amount = Original price × Discount rate

Given that the discount rate is 35% (or 0.35), we have:

Discount amount = P × 0.35

Substituting the discounted price of $6,000, we can write the equation as:

$6,000 = P - (P × 0.35)

Simplifying the equation:

$6,000 = P(1 - 0.35)

$6,000 = P(0.65)

To solve for P, we divide both sides of the equation by 0.65:

P = $6,000 / 0.65

P ≈ $9,230.77

Therefore, the original price of the fencing before the trade discount was approximately $9,230.77.

The correct answer is B. $9,230.77.

Learn more about Price here

https://brainly.com/question/30951540

#SPJ2

Answer:

5 seconds

Step-by-step explanation:

Well we know that when the soccer ball is on the ground the height will be 0.

So we replace y with 0 and solve for x.

0=-12x²+60x

factor out and divide x, (this x is x=0, which is before he kicked it)

0=-12x+60

subtract 60 from both sides

-60=-12x

x=5

Answer:

Question: 1

A dot plot shows individual values. So, we can most easily tell from the dot plot that 5 planes had an average cruising speed of 0.84 Mach

Question: 2

A box plot breaks data into quartiles, each representing 25% of the data. So to find the middle 50% of the data, look at the data that lies between the first and third quartiles of the box plot. The box plot shows that the first and third quartiles are 0.8175 and 0.85, respectively, so 50% of the data lies between 0.8175 and 0.85.

Question: 3

The histogram would be the best data representation for quickly determining how many planes had a speed less than 0.84 Mach. Adding the frequencies of the 3 bins less than 0.84 shows that 17 planes had a speed of less than 0.84 Mach. The dot plot could also be used to determine this, but it would take more time to count each individual dot.

Step-by-step explanation:

answer from plato

Thank me later

The graphical representation which would be best for determining the number of planes that had an average cruising speed of 0.84 Mach is a: histogram.

A histogram can be defined as a type of graph (chart) that is used to graphically represent a data set (statistical information) into user-specified ranges through the use of rectangles.

Generally, the area of each rectangle of a histogram is directly proportional to the data frequency and its width is equal to the class interval.

In this scenario, a histogram is the graphical representation which would be best for determining the number of planes that had an average cruising speed of 0.84 Mach.

Read more on histogram here: brainly.com/question/21304143

Answer:

Problem 1)       [tex] m = \dfrac{1}{4} [/tex]     [tex] slope_{perpendicular} = -4 [/tex]

Problem 2)      [tex] m = \dfrac{1}{3} [/tex]     [tex] slope_{perpendicular} = -3 [/tex]

Step-by-step explanation:

[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex] slope_{perpendicular} = \dfrac{-1}{m} [/tex]

Problem 1) M(9,6), N(1,4)

[tex] slope = m = \dfrac{6 - 4}{9 - 1} = \dfrac{2}{8} = \dfrac{1}{4} [/tex]

[tex] slope_{perpendicular} = \dfrac{-1}{\frac{1}{4}} = -4 [/tex]

Problem 2) M(-2,2), N(4,-4)

[tex] slope = m = \dfrac{4 - 2}{4 - (-2)} = \dfrac{2}{6} = \dfrac{1}{3} [/tex]

[tex] slope_{perpendicular} = \dfrac{-1}{\frac{1}{3}} = -3 [/tex]

Answer:

[tex]\boxed{\sf 10}[/tex]

Step-by-step explanation:

The additive number of any number is the number when added to the number gives a result of zero.

So, if we add 10 to -10 we get a result of zero.

=> -10+10

=> Zero

Answer:

f(-4) = 58

Step-by-step explanation:

Let x = -4:

[tex]f(-4)=3(-4)^2-(-4)+6\\\\f(-4)=3(16)+4+6\\\\f(-4)=48+4+6\\\\f(-4)=58[/tex]

Answer:

56

Step-by-step explanation:

A=(3*4)+(4*(4+3+4))=56

Answer:

w ≥ -18

Step-by-step explanation:

Answer:

w is greater than or equal to-18

Answer:

slope = 2

Step-by-step explanation:

will make it so simple and short

slope = rise / run

slope = 6 / 3

slope = 2

Answer:

B

Step-by-step explanation:

The formula for slope is (y2-y1)/(x2-x1)

In this case it is (1+5)/(3-0)

6/3

2

Answer:

B. FALSE

Step-by-step explanation:

Surface area of cone = πr(r + l)

Where,

r = r

l = 3r

S.A of cone = πr(r + 3r)

= πr² + 3πr²

S.A of cone = 4πr²

Surface area of cylinder = 2πrh + 2πr² = 2πr(h + r)

Where,

r = r

h = 2r

S.A of cylinder = 2πr(2r + r)

= 4πr² + 2πr²

S.A of cylinder = 6πr²

The surface are of the cone and that of the cylinder are not the same. The answer is false.

Answer:false

Step-by-step explanation:

False

Answer:

38.911≤p≤41.089

Step-by-step explanation:

The formula for calculating confidence interval for a population mean us as shown below;

CI = xbar ± Z×S/√N where;

xbar is the sample mean = 40

Z is the z score at 95% confidence interval = 1.96

S is the standard deviation = 5

N is the sample size = 81

Substituting this parameters in the formula we have;

CI = 40±1.96×5/√81

CI = 40±(1.96×5/9)

CI = 40±(1.96×0.556)

CI = 40±1.089

CI = (40-1.089, 40+1.089)

CI = (38.911, 41.089)

The 95% confidence interval for the population mean is 38.911≤p≤41.089

Answer:

38.9 ≤ U ≤ 41.1

Step-by-step explanation:

Mean, m = 40; standard deviation, α = 5; Confidence limit, U = 95% or 0.95

N = 81

The standard error, α(m) = α/√(N) = 5/√81 =5/9

Using table: 0.95 = 0.0379

Z(0.95) = 2 - 0.0379 = 1.9621 or 1.96

Hence, confidence interval = { m - 1.96(α/√N) ≤ U ≤ m +1.96(α/√N)}

But, 1.96(α/√N) = 1.96 X 5/9 = 1.96 X 0.56 = 1.1

(40 - 1.1 ≤ U ≤ 40 + 1.1)

∴ the confidence interval = 38.9 ≤ U ≤ 41.1

Answer:

Option (2)

Step-by-step explanation:

If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.

By using this property,

Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.

By applying Pythagoras theorem in right triangle KNJ,

(KJ)² = (KN)² + (NJ)²

(33)² = (6√10)² + (NJ)²

NJ = [tex]\sqrt{1089-360}[/tex]

NJ = [tex]\sqrt{729}[/tex]

    = 27 units

Since, GJ = 2(NJ)

GJ = 2 × 27

GJ = 54 units

Option (2) will be the answer.

Answer:

His earnings for the period= $123

Step-by-step explanation:

Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.

If 30% of his earnings = $369

His earnings = x

30/100 * x= 369

X= 369*100/30

X= 123*10

X=$ 1230

His earnings for the period= $123

Answer:

8192

Step-by-step explanation:

2 cells at beginning, so the equation is (2)*(2^(4t)) where t is in hours. At the end of 3 hours, the cells will be 2*(2)^(12)=8192

Answer:

  25/4 square inches

Step-by-step explanation:

The area of a sector of a circle is given by the formula ...

  A = (1/2)r²θ

where r is the radius and θ is the central angle in radians.

For your sector, the area is ...

  A = (1/2)(5 in)²(1/2) = 25/4 in²